All Questions
6 questions
-2
votes
1
answer
73
views
How do I keep track of what to differentiate in a Dirac Hamiltonian/Lagrangian?
Suppose we have the dirac Hamiltonian:
$$
H = \int d^3y\bar\psi(y)_b(-i\gamma^k\partial_k+m)_{bc}\psi(y)_c.
$$
My question is should I think the derivative operator $\partial_k$ is acting on the ...
- 1,853
0
votes
1
answer
28
views
Clarification for derivatives under a change of variables
In Special Relativity and Classical Field Theory by Susskind, he says that we can imagine a function of $(x+ct)$, then he says that we can consider its derivatives and easily see that $$\frac{\...
- 1,397
0
votes
1
answer
110
views
Taking the second time derivative of a scalar field
Given some scalar field $\phi(x,y,x,t)$, taking its first total derivative we get:
$$\frac{d\phi}{dt}=\frac{\partial\phi}{\partial t}+\frac{\partial\phi}{\partial x}\frac{dx}{dt}+\frac{\partial\phi}{\...
- 613
1
vote
1
answer
113
views
Calculating the variation of an operator in two different ways
Let
$$
H_{T}=\dot{x}^{I}\frac{\partial}{\partial \psi^{I}}T(x,\psi)
$$
and consider the transformation:
$$
x^{I}\mapsto x^{I}+i\epsilon\psi^{I}
\\
\psi^{I}\mapsto\psi^{I}-2\epsilon\dot{x}^{I}
$$
where ...
- 587
0
votes
1
answer
196
views
Derivative of a complex potential for the $\lambda \Phi^{4}$-model
A charged scalar particle is described by a complex field $\Phi(x) = \phi_{1}(x)+i\phi_{2}(x)$. Consider a Lagrangian of the $\lambda \Phi^{4}$-model whose potential in the Euclidean action is given ...
- 75
0
votes
1
answer
142
views
What's the generator of spinor field shifts?
The shift of a scalar field $\Phi$:
$$ \Phi \rightarrow \Phi'=\Phi - i \epsilon $$
is generated by
$$ G = -i \frac{d}{d\Phi},$$
because
$$ \mathrm{e}^{-i \epsilon \frac{d}{d\Phi} } \Phi = (1-i\...
- 10.3k